Question

The Marbella Hotel is a luxury hotel which has just got a new manager, Jane. Given its location and quality, the hotel always had enough people making advance reservations to fill up all the rooms available. The hotel charges $200 per room per night for reservations made in advance and charges $300 per room per night for last-minute requests. Jane had heard about revenue management in one of the seminars and decided to implement some of those techniques in her current job. Currently, the hotel keeps 3 rooms empty to accommodate last-minute requests. Jane reviewed the records of the last two years and estimated that the number of rooms requested at the last minute is uniformly distributed between 0 and 10.

1)Is the Marbella Hotel maximizing its expected profit by keeping 3 rooms available for last minute requests? What is the optimal number of rooms to reserve for last-minute requests?

Answer 1

Case facts

• The Marbella Hotel is a luxury hotel which has just got a new manager, Jane.
• The hotel charges $200 per room per night for reservations made in advance.
• It charges $300 per room per night for last-minute requests.
• Currently, the hotel keeps 3 rooms empty to accommodate last-minute requests.
• The manager reviewed the records of the last two years and estimated that the number of rooms requested at the last minute is uniformly distributed between 0 and 10.

Problem

a. Is the Marbella Hotel maximizing its expected profit by keeping 3 rooms available for last minute requests? What is the optimal number of rooms to reserve for last-minute requests?

Analysis / Solution

As per the question, following are the purchasing price, selling price, and salvage value.

• Purchasing price = $200
• Selling Price = $300
• Salvage value = $0 (assuming unsold inventory/rooms are worth $0 at the end of the day)

Computations

1. Cu = Cost of underage = Selling Price - Purchasing Cost = $300 - $200 = $100
2. Co = Cost of overage = Purchasing cost - Salvage value = $200 - $0 = $200
3. Optimum service level = critical factor = Cu/(Co + Cu) = 100/(200+100) = 1/3 = 0.333 or 33.3%.
4. Optimal no of rooms to be booked = Q* = 1 + optimal service level *(range of rooms requested) = 1 + 0.333 * (10-0) = 4.33 ~ 4 rooms.

No, the Marbella hotel is not maximizing it’s expected profit by keeping 3 rooms available for last-minute requests.

Marbella hotels should keep 4 rooms as an Optimal number of rooms to reserve for last-minute requests to maximize their profits.